How is it damaged ? Scratches in CDs/DVDs can be buffed out with Brasso or something similar, but if you have cracks, missing bits, or missing data that's more problematic. Probably a sling & repurchase job.
(If it is simply not reading then maybe a recovery ap might work.)
OG - Seems to go so far and then a blank screen.....No obvious major damage...appears slightly scuffed.- My usual remedy is to rinse under the tap with some washing liquid. Not tried brasso!
After cleaning a CD/DVD disk you can always try a small amount of car body type wax which may fill in the scratches sufficiently to make it work.
Incidentally, it always pays to make a copy of the original system disks before installing the system or program then you'll always have a back-up and won't have to buy a replacement.